Average Error: 6.3 → 0.2
Time: 9.8s
Precision: 64
$\frac{k}{\left(\left(f \cdot f\right) \cdot f\right) \cdot f}$
${f}^{-2} \cdot \frac{k}{{f}^{2}}$
\frac{k}{\left(\left(f \cdot f\right) \cdot f\right) \cdot f}
{f}^{-2} \cdot \frac{k}{{f}^{2}}
double f(double k, double f) {
double r1472864 = k;
double r1472865 = f;
double r1472866 = r1472865 * r1472865;
double r1472867 = r1472866 * r1472865;
double r1472868 = r1472867 * r1472865;
double r1472869 = r1472864 / r1472868;
return r1472869;
}


double f(double k, double f) {
double r1472870 = f;
double r1472871 = -2.0;
double r1472872 = pow(r1472870, r1472871);
double r1472873 = k;
double r1472874 = 2.0;
double r1472875 = pow(r1472870, r1472874);
double r1472876 = r1472873 / r1472875;
double r1472877 = r1472872 * r1472876;
return r1472877;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 6.3

$\frac{k}{\left(\left(f \cdot f\right) \cdot f\right) \cdot f}$
2. Simplified6.2

$\leadsto \color{blue}{\frac{k}{{f}^{4}}}$
3. Using strategy rm

$\leadsto \frac{k}{{\color{blue}{\left(\sqrt{f} \cdot \sqrt{f}\right)}}^{4}}$
5. Applied unpow-prod-down35.1

$\leadsto \frac{k}{\color{blue}{{\left(\sqrt{f}\right)}^{4} \cdot {\left(\sqrt{f}\right)}^{4}}}$
6. Applied *-un-lft-identity35.1

$\leadsto \frac{\color{blue}{1 \cdot k}}{{\left(\sqrt{f}\right)}^{4} \cdot {\left(\sqrt{f}\right)}^{4}}$
7. Applied times-frac32.1

$\leadsto \color{blue}{\frac{1}{{\left(\sqrt{f}\right)}^{4}} \cdot \frac{k}{{\left(\sqrt{f}\right)}^{4}}}$
8. Simplified32.0

$\leadsto \color{blue}{\frac{1}{{f}^{2}}} \cdot \frac{k}{{\left(\sqrt{f}\right)}^{4}}$
9. Simplified0.2

$\leadsto \frac{1}{{f}^{2}} \cdot \color{blue}{\frac{k}{{f}^{2}}}$
10. Using strategy rm
11. Applied pow-flip0.2

$\leadsto \color{blue}{{f}^{\left(-2\right)}} \cdot \frac{k}{{f}^{2}}$
12. Simplified0.2

$\leadsto {f}^{\color{blue}{-2}} \cdot \frac{k}{{f}^{2}}$
13. Final simplification0.2

$\leadsto {f}^{-2} \cdot \frac{k}{{f}^{2}}$

# Reproduce

herbie shell --seed 1
(FPCore (k f)
:name "k / (f*f*f*f)"
:precision binary64
(/ k (* (* (* f f) f) f)))